Matricial characterization of tournaments with maximum number of diamonds

2019/06/11 by Belkouche, Wiam, Boussaïri, Abderrahim, Lakhlifi, Soufiane +1 · 2 citations
#05B20 #05C20 #05C35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.04672

Abstract

A diamond is a 4-tournament which consists of a vertex dominating or dominated by a 3-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of n-tournaments with the maximum number of diamonds when n≡0\pmod4 and n≡3\pmod4. For n≡2\pmod4, we obtain an upper bound on the number of diamonds in an n-tournament and we give a matricial characterization of tournaments achieving this bound.

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